Write an equation for the translation of x 2 + y 2 = 16 by 8 units left and 3 units down.
I bet you mean
x^2 + y^2 = 16
well we could do it right or we could cheat and say we want a circle with center at (-8 ,-3)
(x+3)^2 + (y+3)^2 = 4^2
42
To translate the equation x^2 + y^2 = 16 by 8 units left and 3 units down, you need to adjust the coordinates of each point on the graph accordingly.
First, let's focus on the horizontal translation. Moving 8 units to the left means that the x-coordinate of each point will decrease by 8. To account for this, subtract 8 from the original x-coordinate.
Secondly, for the vertical translation, moving 3 units down means that the y-coordinate of each point will decrease by 3. To represent this shift, subtract 3 from the original y-coordinate.
Therefore, the equation for the translated graph will be:
(x - 8)^2 + (y - 3)^2 = 16
To translate a given equation by a certain amount left or right and up or down, we need to apply the corresponding changes to the variables. In this case, we want to translate the equation x^2 + y^2 = 16 by 8 units left and 3 units down.
To move an equation 8 units left, we subtract 8 from the x-variable. To move it 3 units down, we subtract 3 from the y-variable. So, the translation equation can be written as:
(x - 8)^2 + (y - (-3))^2 = 16
Simplifying further, we have:
(x - 8)^2 + (y + 3)^2 = 16
And this is the equation for the translation of x^2 + y^2 = 16 by 8 units left and 3 units down.